In the face of ongoing global climate and land use change, organisms have multiple possibilities to cope with the modification of their environment. The two main possibilities are to either adapt locally or disperse to a more suitable habitat. The evolution of both local adaptation and dispersal interacts and can be influenced by the spatial and temporal variation (of e.g. temperature or precipitation). In an individual based model (IBM), we explore evolution of phenotypes in landscapes with varying degree of spatial relative to global temporal variation in order to examine its influence on the evolution of dispersal, niche optimum and niche width. The relationship between temporal and spatial variation did neither influence the evolution of local adaptation in the niche optimum nor of niche widths. Dispersal probability is highly influenced by the spatio‐temporal relationship: with increasing spatial variation, dispersal probability decreases. Additionally, the shape of the distribution of the trait values over patch attributes switches from hump‐ to U‐shaped. At low spatial variance more individuals emigrate from average habitats, at high spatial variance more from extreme habitats. The comparatively high dispersal probability in extreme patches of landscapes with a high spatial variation can be explained by evolutionary succession of two kinds of adaptive response. Early in the simulations, extreme patches in landscapes with a high spatial variability act as sink habitats, where population persistence depends on highly dispersive individuals with a wide niche. With ongoing evolution, local adaptation of the remaining individuals takes over, but simultaneously a possible bet‐hedging strategy promotes higher dispersal probabilities in those habitats. Here, in generations that experience extreme shifts from the temporal mean of the patch attribute, the expected fitness becomes higher for dispersing individuals than for philopatric individuals. This means that under certain circumstances, both local adaptation and high dispersal probability can be selected for for coping with the projected environmental changes in the future.